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Well, the first mistake was deciding you knew better than the PT.
The second mistake was continuing to do back-straining (and hip-straining) exercises despite being injured.
Instead of feeling like the only purpose of your gym membership is to have HUUUUUGGGE MUUUUUSSSSSCLES, how about doing your assigned PT exercises, light weight lifting of the areas that you are cleared for by the PT, stretching, yoga classes, and aerobic exercise? I am sure the gym has staffers who are accustomed to working with people who have PT prescriptions, and it will be a heck of a lot easier to set up the machines to do the exercises there, than to try to replicate the setup at home.